Ensure you have the x86 version of Java installed, even on a 64-bit Windows OS.
The Cisco community documented several workarounds: Cisco Configuration Professional 2.6 x86
Use CCP 2.6 strictly for migration —to extract running configs or to visually understand an old topology. For ongoing management, learn the CLI or upgrade to a 64-bit management tool like Cisco Configuration Professional Express (embedded in the router). Ensure you have the x86 version of Java
However, Cisco Configuration Professional 2.6 is generally provided as a for Cisco customers. You typically do not need a paid license key to run the application itself; rather, you need a valid Cisco Connection Online (CCO) account to download it. 🔑 How to Access CCP 2.6 Cisco Configuration Professional 2.6 x86
Release Notes For Cisco Configuration Professional 2.0 - Scribd